RIGID PARTICLES IN AN ELASTIC POLYMER NETWORK - AN ELECTRICAL-ANALOG APPROACH

Within the Gaussian phantom-chain model of a polymer network, we demon strate and apply the formal analogy between the problem of computing t he force constants acting on a set of rigid filler particles and that of computing the capacity of a system of conductors in a dielectric me dium. We find that a single spherical particle undergoes a mean-square displacement [(Delta X)(2)] from its equilibrium position which is in versely proportional to its radius R. It is thus subject to an isotrop ic harmonic potential with force constant [3k(B)T/[(Delta X)(2)]] prop ortional to R. Quantitative evaluation of the proportionality constant for typical unswollen networks shows that root[(Delta X)(2)]/R decrea ses from 10(-1) to 10(-5) as R increases from 10 nm to 1 mu m. The tim e scale of these fluctuations is independent of R and falls in the ran ge 10(-4)-10(1) s. The fluctuations of two neighboring particles are n ot additive. A distance-dependent ''stiffening'' of the network is dem onstrated through the calculation of the appropriate response and forc e constant matrices. (C) 1998 American Institute of Physics. [S0021-96 06(98)50131-6]